Question

IG6 P5.29 You have three portfolios containing four assets each. The following table specifies the weights assigned to each asset in each of the three portfolios, along with each asset's beta: Asset Asset Beta 1.5 Portfolio A 30% Portfolio Weights Portfolio B 5% bobobsle B 0 . C lib pob D 1.8 0.30 -0.40 40% 20% 10% 100% 15% 30% 50% 100% Portfolio C 35% 5% 40% 20% 100% n old a. Calculate the betas for the three portfolios. b. Rank the portfolios from the highest risk to the lowest risk according to their betas.

Answer 1

(a) Betas of the three portfolios are as follows:

Portfolio A: 1.19

Portfolio B: 0.235

Portfolio C: 0.655

These are arrived at as the sum of the products of betas of individual assets in the portfolio, multiplied by their respective proportions.

Detailed working as follows:

1 Asset 2 I B C D E F G H Asset Beta Portfolio A Portfolio B Portfolio C Weight (w) W*b Weight (w) W*b Weight (w) W*b 30% 0.45 5% 0.075 0.525 1.8 40% 0.72 15% 0.27 5% 0.09 20% 0.06 30% 0.09 40% 0.12 -0.4 10% -0.04 50% -0.2 20% -0.08 100% 1.190000 100% 0.235000 100% 0.655000 3 A 4 B 5c 1.5 0.3 6 D 7 Total

(b) Beta is the measure of degree of change in the asset value, corresponding to the change in the value of benchmark. Hence Beta measures the volatility of risk, the higher the more risk. Accordingly, portfolios A, B and C are ranked as follows:

Highest risk: Portfolio A with highest beta of 1.19

Second highest risk: Portfolio C with beta of 0.655

Lowest risk: Portfolio B with lowest beta of 0.235